Wednesday, 14 June 2017

A trigonometry exercise $2sin frac{pi}{14}+2sin frac{5pi}{14}-2sin frac{3pi}{14}=1$

How to prove that



$$2\sin \frac{\pi}{14}+2\sin \frac{5\pi}{14}-2\sin \frac{3\pi}{14}=1$$




I absolutely have no idea other than using the property
$\sin\bigl(\frac{\pi}{2}-a\bigr)=\cos a\;$

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